5.1 probability in our daily lives. which of these list is a “random” list of results when...
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Chapter Five5.1 Probability in our Daily Lives
Which of these list is a “random” list of results when flipping a fair coin 10 times?
A) T H T H T H T H T H B) T T H T H T T H H T C) H H H H H H H H H
Answer: D) All of the above!
What is Random?
With a small number of trials the outcome of random events can vary widely from what we expect them to be.
Examples:◦ Coin Flips◦ Winning Streaks◦ Others
Probability:
However with a Large number of event, Called Trials, the proportion of times the event occurs will become more predictable.
Examples:◦ Casino games◦ Others
Probability:
With a randomized experiment, the probability of a particular outcome is the proportion of times that outcome would occur in a long run of observations.
◦ Outcome: The result of a specific trial.
◦ Long run: Very large, often theoretically large, number of trials.
Law of Large Numbers:
We are going to try a few coin flips: Flip One: Tails Flip Two: Heads Flip Three: Heads Flip Four: Heads Flip Five: Heads Flip six: Heads
No matter what happened before the odds will always be 50::50.
Independence:
Different trials of a random phenomenon are independent if the outcome of any one trial is not effected by the outcome of any other trial.
Independent Examples:
Dependent Examples:
Independent Trials:
1) Logic, symmetry, structure. Best for simple well understood situations.
2) Sample trials. Good for complex situations we can model.
Finding Probabilities:
Next Time Finding Probabilities.
“What is the chance of rolling at least one 6 on six roles?”